Two fuel additives are tested to determine their effect on miles per gallon for passenger cars. Test results for 12 cars follow; each car was tested with both fuel additives.AdditiveCar12119.1217.0522.5620.773.21.0321.57419.1517.0621.2321.2225.7722.816.1616.2818.5514.9821.8720.031023.2321.151122.2121.781225.0222.7Use a = .05 and the Wilcoxon signed-rank test to see whether there is a significant difference between the median miles per gallon for the additives. Use Table 1 of AppendixВ. a. What are the null and alternative hypotheses?Ho : Median for Additive 1 – Median for Additive 2 equal to 0Ha : Median for Additive 1- Median for Additive 2 not equal to 0b. What is the mean and standard deviation of the normal distribution that can be used for this statistical test (to 4 decimals if necessary)?MeanStandard deviationc. What is the value of the test statistic (to 2 decimals)?What is the p-value for the hypothesis test (to 4 decimals)?Conclude:There is a significant difference in the median miles per gallon for the two additives.

First compute the difference between the data of the additives. Following table gives the difference between each pair of additives. Additive 1 Additive 2 Difference 19.12 17.05 2.07 22.56 20.77 1.79 21.03 21.57 -0.54 19.15 17.06 2.09 21.23 21.22 0.01 25.77 22.8 2.97 16.16 16.2 -0.04 18.55 14.98 3.57 21.87 20.03 1.84 23.23 21.15 2.08 22.21 21.78 0.43 25.02 22.7 2.32Arrange these difference in ascending order according to their absolute value and rank them. Difference Absolute value Sign Rank 0.01 0.01 + 1 -0.04 0.04 - 2 0.43 0.43 + 3 -0.54 0.54 - 4 1.79 1.79 + 5 1.84 1.84 + 6 2.07 2.07 + 7 2.08 2.08 + 8 2.09 2.09 + 9 2.32 2.32 + 10 2.97 2.97 + 11 3.57 3.57 + 12The rank 2 and 4 has negative sign and other ranks has positive sign. These signs are according to the difference, if the difference is negative then the sign for the rank is negative and if the difference is positive then the sign is positive. Now compute the sum of the ranks for positive signs and negative signs. W-=2+4=6W+=1+3+5+6+7+8+9+10+11+12=72The value of W- has value smaller than W+, so the test statistic will be equal to the value of W- that is 6. So test statistic has value 6. The mean and standard deviation is given by μ=n(n+1)4 and σ=n(n+1)(2n+1)24 where n is the number of observations. There total 12 observations in each sample so n=12. Substitute the value and find the mean and standard deviation. μ=12(12+1)4=12×134=39σ=12(12+1)(2×12+1)24=12×13×2524=162.5≈12.7475 So mean is 39 and standard deviation is 12.7475. Now find the z score using z=Test statistic-μσ. Substitute 6 as test statistic, mean μ=39 and standard deviation σ=12.7475 z=6-3912.7475=-3312.7475≈-2.5887The alternate hypothesis claims that the difference in median is not equal to 0 so it can be more than or less than 0, thus the test will be two tailed. From the z table, the probability for z<-2.5887 or left tail is 0.0048. For two tailed the P value will be equal to twice of 0.0048. P-value=2×0.0048=0.0096 The P value is 0.0096 which is smaller than 0.05 significance level, thus the null hypothesis can be rejected. So it can be concluded that there is significant evidence of difference in median.

Math

Statistics

Two fuel additives are tested to determine their effect on miles per gallon for passenger cars. Test results for 12 cars follow; each car was tested with both fuel additives. Additive Car 1 19.12 17.05 2. 22.56 20.77 3 21.03 21.57 4. 19.15 17.06 21.23 21.22 6. 25.77 22.8 7. 16.16 16.2 18.55 14.98 9. 21.87 20.03 10 23.23 21.15 11 22.21 21.78 12 25.02 22.7 Use a = .05 and the Wilcoxon signed-rank test to see whether there is a significant difference between the median miles per gallon for the additives. Use Table 1 of Appendix В.

Two fuel additives are tested to determine their effect on miles per gallon for passenger cars. Test results for 12 cars follow; each car was tested with both fuel additives. Additive Car 1 19.12 17.05 2. 22.56 20.77 3 21.03 21.57 4. 19.15 17.06 21.23 21.22 6. 25.77 22.8 7. 16.16 16.2 18.55 14.98 9. 21.87 20.03 10 23.23 21.15 11 22.21 21.78 12 25.02 22.7 Use a = .05 and the Wilcoxon signed-rank test to see whether there is a significant difference between the median miles per gallon for the additives. Use Table 1 of Appendix В.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster.
Phosphorous is a chemical that is found in many household cleaning products. Unfortunately, phosphorous also finds its way into surface water, where it can harm fish, plants, and other wildlife. Two methods of phosphorous reduction are being studied. At a random sample of 7 locations, both methods were used and the total phosphorous reduction (mg/L) was recorded. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. Things that are labelled i underneath a b c, etc are all part of that part.
Find the test statistic for a proportion "p" given the following information. Malloree ordered 15 pair of shoes online during the stay-at-home order, and 2 pairs arrived with mismatched sizes. Looking on line, she found that the retailer claimed that this happened 4% of the time with online orders. Enter your answer rounded to the thousandths place.
A researcher wants to find the effect of a special diet on systolic blood pressure. A sample of 7 adults was selected to start them on this diet for 3 months. Based on this information, can it be stated that systolic blood pressure changes with the special diet? The test statistic that will determine whether systolic blood pressure changes with the special diet is...... A. 1.23 B. 0.48 C. 18.1 D. 21.08 E. 4.08
answer blank
Phosphorous is a chemical that is found in many household cleaning products. Unfortunately, phosphorous also finds its way into surface water, where it can harm fish, plants, and other wildlife. Two methods of phosphorous reduction are being studied. At a random sample of 7 locations, both methods were used and the total phosphorous reduction (mg/L) was recorded. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. Site 1 2 3 4 5 6 7 Method I: 0.013 0.020 0.015 0.055 0.007 0.002 0.010 Method II: 0.014 0.045 0.017 0.039 0.017 0.001 0.013 Do these data indicate a difference (either way) in the average reduction of phosphorous between the two methods? Use α = 0.05. (Let d = Method I − Method II.) (i) What is the level of significance? What is the value of the sample test statistic? (Round…
In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance. City: 16.7 17.2 16.4 14.9 13.7 15.8 17.3 16.5 16.6 15.8 15.7 15.8 16.7 Highway: 20.0 21.2 18.9 19.2 19.8 18.0 17.8 19.2 19.6 21.7 20.0 19.1 19.3 Calculate the mean, median, and mode for City and Highway gasoline consumption (to 1 decimal). City Highway Mean Median Mode The data are bimodal: and
A random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen, resulting in the accompanying data. 1.16 5.09 0.97 1.59 4.60 0.32 0.55 1.45 0.16 4.47 1.20 3.50 5.02 4.67 5.22 2.69 3.97 3.17 3.03 2.21 0.69 4.47 3.31 1.17 0.77 1.17 1.57 2.62 1.66 2.05 The values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2.484, 1.612, and 0.294, respectively. Does this data suggest that the true average percentage of organic matter in such soil is something other than 3%? Carry out a test of the appropriate hypotheses at significance level 0.10. [Note: A normal probability plot of the data shows an acceptable pattern in light of the reasonably large sample size.] State the appropriate hypotheses. ⒸH₁: μ = 3 H₂:μ # 3 OH:μ #3 Ha: μ 3 t = P-value = Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal…
The average spent nationally on Christmas gifts in 2020 was reported to be $650 per person. Below is a random sample of gift givers from Iowa and what they spent in 2020. Is there sufficient evidence to conclude that Iowans spend less than the national average? Estimate the average amount spent by Iowans on Christmas gifts in 2020 with a 90%-CI. 700 450 400 525 550 550 600 575 650 625 500
your car is more crowded than you think. table 5.8 reports results from a 1969 personal transportation survey on "home-to-work" trips in metropolitan areas. The survey stated that the average car occupancy was 1.4 people. check that calculation.